Stochastic simulations of high { Reynolds { number turbulence intwo
نویسنده
چکیده
The dynamics of the two{dimensional turbulence is studied by a stochastic simulation method. The latter is based on a representation of the random vorticity eld and stream function by a multivariate stochastic process de-ned by a discrete master equation. It is demonstrated that in the continuum limit the complete hierarchy of coupled moment equations for the statistical formulation of the 2D Navier{Stokes equation is obtained. The probabilistic time{evolution leads to random stresses which can be traced to thermal uc-tuations and allow to disentangle hydrodynamic and thermodynamic degrees of freedom by some kind of renormalization procedure. The stochastic simulations at a large scale Reynolds number of 2:510 5 clearly show the existence of a k ?3 power law in the inertial range of the energy spectrum as is predicted by the Kraichnan{Batchelor theory.
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